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All Journal Jurnal Sosiologi Reflektif Majalah Kedokteran Sriwijaya Paedagoria : Jurnal Kajian, Penelitian dan Pengembangan Kependidikan Beta: Jurnal Tadris Matematika Jurnal Ilmiah Profesi Pendidikan Griya Journal of Mathematics Education and Application Rengganis Jurnal Pengabdian Masyarakat Kontribusi: Jurnal Penelitian dan Pengabdian Kepada Masyarakat Prosiding Konferensi Nasional PKM-CSR Jurnal Pijar MIPA Al-Irsyad Journal of Mathematics Education International Journal of Computing Science and Applied Mathematics-IJCSAM
Laila Hayati
Universitas Mataram
Religion Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Engineering Environmental Science Health Professions Law, Crime, Criminology & Criminal Justice Mathematics Medicine & Pharmacology Nursing Physics Public Health Social Sciences

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Partition Dimension of Bridge Graphs Between Complete and Star Graphs Amrullah Amrullah; Laila Hayati; Junaidi Junaidi
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 11 No. 2 (2025)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v11i2.8363

Abstract

This paper investigates the determination of the partition dimension for a \emph{bridge graph} formed by connecting a clique $K_n$ and a star $K_{1,m}$ through a single edge. Although the partition dimension has been extensively studied for various families and graph operations, the mixed dense--sparse case on $B(K_n,K_{1,m})$ remains unsettled, since the result is sensitive to the position of the bridge edge and the balance between the size parameters $n$ and $m$.We combine distance symmetry arguments, leaf-based constraints at the star center, and explicit constructions of distinguishing partitions to obtain tight values of the partition dimension. The study begins with the basic cases $K_1$ and $K_2$, and then proceeds to the general case with parameters $n\ge 2$. The main result shows that for the \emph{central bridge} ($e=v_1x$), it holds that $pd(B)=n-1$ if $m<n$, $pd(B)=n$ if $m=n$, and $pd(B)=m$ if $m>n$; for the \emph{leaf bridge} ($e=v_1u_1$), it holds that $pd(B)=n$ when $m\le n$, and$pd(B)=m-1$ when $m>n$. These results demonstrate that the location of the bridge edge, together with the size parameters $m$ and $n$ of the components, can sharpen the partition dimension value of the graph prior to the bridging operation.
Co-Authors Aena Malini Amrullah Amrullah Amrullah Amrullah Arjudin Arjudin Athuf Thaha Baidowi Baidowi Baiq Noviana Ekawati Baiq Suhadiati Handini Bq. Nerik Prawita Bustami Rahman Dwi Novitasari Dwi Novitasari Eka Kurniawan Emi Lara Safitri Esti Winda Sari Faridatul Wardi Faturahman Faturahman Gossani Puja Lestari Hapipi Hapipi Harry Soeprianto Herdiyanti, Herdiyanti Herman Firdaus I Gede Adhitya Wisnu Wardhana Ika Kurniawati Intan Rachmawati Iqrimi Ziarati Ivon Prawita Junaidi Junaidi Ketut Sarjana Khafifah Ulumul Azri Kunim Sriati Linda Lestari Luna Febriani M. Adzan Akbar M. Khairul Miswari M. Satria Ramanda Mahyarani Mahyarani Mamika Ujianita Romdhini Mamika Ujianita Romdhini Mariya Sulastri Maysya Rizky Tri Juliana Muhamad Turmuzi Muhammad Arifuddin Muhammad Turmuzi Muhammda Faisal Khatami Munawarah Munawarah Mursali Wirejati Akbar Nani Kurniati NI MADE INTAN KERTIYANI Ni Made Intan Kertiyani Ni Nyoman Sriningsih Ni Nyoman Yustini Wikantari Nina Niarti Nunung Rusdiyawanti Nur Asiah Nur Wahyuningsih Nurhafizah Nurhafizah Nurlailis Kurniawati Nyoman Sridana Panggio Restu Wilujeng Patria Susetya Prangga Assmarqandi Putra Pratama Saputra R.M. Suryadi Tjekyan Ramlah Ramlah Rani Rizka Ramdani Riani Permatasari Rina Ardianti Rukmana Riska Dwi Setiawati Rosfita Karolina Salsabila, Nilza Humaira Sibtil Hasaniah Silma Safira Hifyatin Silvia Rizki Ayu Ningsih Siti Raudhatul Kamali Sri Subarinah Sripatmi Sripatmi Sudi Prayitno Surahman Surahman Surya Hadi Syahrul Azmi Syatia Perwira Darmawansyah Tabita Wahyu Triutami Tantawi D Tantawi D Tri Muhammad Rahmatullah Ulfa Lu’luilmaknun Ulfa Lu’luilmaknun Uswatun Hasanah Wahidaturrahmi, Wahidaturrahmi Warnawati Warnawati Yuliana Yulis Tyaningsih, Ratna Yunita Ramdani